You have a lock in front of you with 4 circular wheels. Each wheel has 10 slots: ‘0’, ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, ‘6’, ‘7’, ‘8’, ‘9’. The wheels can rotate freely and wrap around: for example we can turn ‘9’ to be ‘0’, or ‘0’ to be ‘9’. Each move consists of turning one wheel one slot.
The lock initially starts at ‘0000’, a string representing the state of the 4 wheels.
You are given a list of deadends dead ends, meaning if the lock displays any of these codes, the wheels of the lock will stop turning and you will be unable to open it.
Given a target representing the value of the wheels that will unlock the lock, return the minimum total number of turns required to open the lock, or -1 if it is impossible.
Example 1:
Input: deadends = [“0201”,”0101”,”0102”,”1212”,”2002”], target = “0202” Output: 6 Explanation: A sequence of valid moves would be “0000” -> “1000” -> “1100” -> “1200” -> “1201” -> “1202” -> “0202”. Note that a sequence like “0000” -> “0001” -> “0002” -> “0102” -> “0202” would be invalid, because the wheels of the lock become stuck after the display becomes the dead end “0102”. Example 2:
Input: deadends = [“8888”], target = “0009” Output: 1 Explanation: We can turn the last wheel in reverse to move from “0000” -> “0009”. Example 3:
Input: deadends = [“8887”,”8889”,”8878”,”8898”,”8788”,”8988”,”7888”,”9888”], target = “8888” Output: -1 Explanation: We can’t reach the target without getting stuck. Example 4:
Input: deadends = [“0000”], target = “8888” Output: -1
Constraints:
1 <= deadends.length <= 500 deadends[i].length == 4 target.length == 4 target will not be in the list deadends. target and deadends[i] consist of digits only.
Solution:
class Solution {
vector<int> deadends;
static int to_index(const string& s) {
return (s[0] - '0') * 1000 +
(s[1] - '0') * 100 +
(s[2] - '0') * 10 +
(s[3] - '0');
}
static vector<int> adjacent_digit(int digit) {
vector<int> v;
v.push_back((digit + 1) % 10);
v.push_back((digit + 9) % 10);
return v;
}
static vector<int> adjacent_index(int index) {
int d3 = index / 1000;
int d2 = (index / 100) % 10;
int d1 = (index / 10) % 10;
int d0 = index % 10;
vector<int> v;
for (int d3a : adjacent_digit(d3))
v.push_back(d3a * 1000 + d2 * 100 + d1 * 10 + d0);
for (int d2a : adjacent_digit(d2))
v.push_back(d3 * 1000 + d2a * 100 + d1 * 10 + d0);
for (int d1a : adjacent_digit(d1))
v.push_back(d3 * 1000 + d2 * 100 + d1a * 10 + d0);
for (int d0a : adjacent_digit(d0))
v.push_back(d3 * 1000 + d2 * 100 + d1 * 10 + d0a);
return v;
}
public:
int openLock(vector<string>& deadends, string target) {
bool visited[10000] = {false};
for (const auto& deadend : deadends) visited[to_index(deadend)] = true;
if (to_index(target) == 0) return 0;
if (visited[0]) return -1;
visited[0] = true;
int len = 0;
set<int> explore;
explore.insert(0);
while (!explore.empty()) {
++len;
set<int> explore_next;
for (int current : explore) {
vector<int> a = adjacent_index(current);
for (int next : a) {
if (next == to_index(target)) return len;
if (visited[next]) continue;
explore_next.insert(next);
visited[next] = true;
}
}
explore = explore_next;
}
return -1;
}
};